* Shakeout complete, dollar index back at pre-payrolls highs
* Data restoring faith in U.S. recovery, CPI next in focus
* Aussie dives 1.2 pct to hit lowest since Aug 2010
* Canadian dollar also seen soft ahead of BoC meeting next week
SYDNEY/TOKYO, Jan 16 (Reuters) - The U.S. dollar held firm on Thursday, having returned to levels seen before last week's soft payrolls data as faith in the U.S. economic recovery was restored, while the Australian dollar slid to a 3-1/2-year low after a dismal local jobs report.
Upbeat U.S. numbers this week held out hope that Friday's surprisingly soft employment data was an anomaly and did not signal the economy had lost steam at the end of last year.
U.S. data on Wednesday showed producer prices recorded their largest gain in six months in December, yet there were few signs of any sustained price pressures. The figures came a day after U.S. retail sales rose and a core spending gauge posted a big jump.
Investors were encouraged to go long on the greenback, again betting the Federal Reserve can continue to unwind its massive bond-buying stimulus over 2014. They pushed the dollar index back to the highs seen last Friday.
Also helping the dollar, one of the Federal Reserve's most outspoken doves, Chicago Fed President Charles Evans, said he backed a continued wind-down of the Fed's bond-buying programme and could even see bigger cuts to the programme if the economy strengthens.
Against the yen, the dollar bounced to 104.74, within striking distance of a five-year peak of 105.45 yen scaled at the start of the year.
But some traders said there were sizable offers above that level, possibly capping the dollar's gains in the near term.
Traders also said U.S. consumer inflation data due later on Thursday would be closely watched.
"A strong inflation print may encourage the Federal Open Market Committee to take a more aggressive approach in normalising monetary policy as the central bank sees a more robust recovery in 2014," said David Song, analyst at DailyFX.
"With that said, a positive CPI print may spark a bullish reaction in the USD, but the dollar may face a larger decline over the near-term should the data print fall short of market expectations."
The euro skidded to $1.3605, having touched a near one-week low of $1.3581 overnight.
The Australian dollar slid more than 1 percent to as low as $0.8797 - its lowest since August 2010 - after dismal Australian employment data revived expectations of an interest rate cut by the Reserve Bank of Australia.
Employers shed jobs at the fastest pace in nine months in December, with full-time positions hit hard in particular, contrary to economists' expectations of modest job gains .
Investors reacted by reviving the prospect of another cut in interest rates from the Reserve Bank of Australia, which has been signalling it would rather not ease again from the current record low of 2.5 percent.
The Aussie last stood at $0.8815, having fallen 3 percent from Monday's high of $0.9087, with the next key level seen around $0.8775, the 76.4 percent retracement of the currency's long-term rally from 2010 to 2011.
The Canadian dollar was on a similar trajectory despite its small rebound on Wednesday, due to speculation the Bank of Canada could step towards an easing bias following a string of weak domestic data.
The Canadian dollar stood at C$1.0963 to the U.S. dollar , near a four-year low of C$1.0992 hit on Wednesday.
"The Canadian policy rate is among the highest of the G10 countries and a lot of people are now questioning if that is sustainable," said Kyosuke Suzuki, director of forex at Societe Generale in Tokyo. "The market will test the big level of C$1.10 ahead of the Bank of Canada's rate decision on Jan. 22. It is a matter of time."